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 A211183 Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1, 1, 3, 3, 6, 6, 10, 10, 15, ...) DELTA (1, 0, 2, 0, 3, 0, 4, 0, 5, ...) where DELTA is the operator defined in A084938. 5
 1, 0, 1, 0, 1, 1, 0, 2, 4, 1, 0, 7, 19, 11, 1, 0, 38, 123, 107, 26, 1, 0, 295, 1076, 1195, 474, 57, 1, 0, 3098, 12350, 16198, 8668, 1836, 120, 1, 0, 42271, 180729, 268015, 176091, 52831, 6549, 247, 1, 0, 726734, 3290353, 5369639, 4105015, 1564817, 287473, 22145 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Paul D. Hanna, Rows n = 0..31, flattened. FORMULA Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A000012(n), A000366(n+1), A110501(n+1), A211194(n), A221972(n) for x = 0, 1, 2, 3, 4 respectively. T(n,n-1) = A000295(n). T(n,1) = A000366(n). G.f.: A(x,y) = Sum_{n>=0} n! * x^n * Product_{k=1..n} (y + (k-1)/2) / (1 + (k*y + k*(k-1)/2)*x). - Paul D. Hanna, Feb 03 2013 EXAMPLE Triangle begins : 1; 0, 1; 0, 1, 1; 0, 2, 4, 1; 0, 7, 19, 11, 1; 0, 38, 123, 107, 26, 1; 0, 295, 1076, 1195, 474, 57, 1; 0, 3098, 12350, 16198, 8668, 1836, 120, 1; 0, 42271, 180729, 268015, 176091, 52831, 6549, 247, 1; 0, 726734, 3290353, 5369639, 4105015, 1564817, 287473, 22145, 502, 1; ... PROG (PARI) T(n, k)=polcoeff(polcoeff(sum(m=0, n, m!*x^m*prod(k=1, m, (y + (k-1)/2)/(1+(k*y+k*(k-1)/2)*x+x*O(x^n)))), n, x), k, y) for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print()) \\ Paul D. Hanna, Feb 03 2013 CROSSREFS Cf. A000366, A110501, A211194, A221972. Sequence in context: A294390 A152433 A094344 * A137391 A276207 A248672 Adjacent sequences:  A211180 A211181 A211182 * A211184 A211185 A211186 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Feb 02 2013 STATUS approved

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Last modified September 19 15:43 EDT 2020. Contains 337178 sequences. (Running on oeis4.)